TY - THES A1 - Nowak, Ulrich T1 - Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension. N2 - A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi--implicit Euler discretization. Space discretization is done with finite differences on non--uniform grids. Both basic discretizations are coupled with extrapolation techniques. With respect to time the extrapolation is of variable order whereas just one extrapolation step is done in space. Based on local error estimates for both, the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously. Besides the local adaptation of the space grids after each integration step (static regridding), the grid may even move within each integration step (dynamic regridding). Thus, the whole algorithm has a high degree of adaptivity. Due to this fact, challenging problems from applications can be solved in an efficient and robust way. T3 - ZIB-Report - TR-93-14 Y1 - 1993 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/505 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-5059 ER -